Amplituhedra, Cluster Algebras, and Positive Geometry


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May 29, 2024 - May 31, 2024 9:00 am - 5:00 pm
CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138

Amplituhedra, Cluster Algebras, and Positive Geometry

Dates: May 29-31, 2024

Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138 & via Zoom

In recent years, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously, cluster algebras, originally introduced by Fomin and Zelevinsky to study total positivity, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries, and in particular to the amplituhedron. Additionally, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT.

The conference features: Introductory Lectures, an Open Problems Forum, Emerging Scholars Talks, and talks by experts in the fields.

See the detailed schedule on the conference webpage.

Directions to CMSA

Register Online for in-person talks

Register for Zoom Meeting

Confirmed Speakers:

  • Evgeniya Akhmedova, Weizmann Institute of Science
  • Nima Arkani-Hamed, IAS
  • Paolo Benincasa, MPI
  • Nick Early, Weizmann Institute of Science
  • Carolina Figueiredo, Princeton University
  • Yu-tin Huang, National Taiwan University
  • Dani Kaufman, University of Copenhagen
  • Chia-Kai Kuo, National Taiwan University
  • Thomas Lam, University of Michigan
  • Yelena Mandelshtam, UC Berkeley
  • Shruti Paranjape, UC Davis
  • Elizabeth Pratt, UC Berkeley
  • Lecheng Ren, Brown University
  • Sebastian Seemann, KU Leuven
  • Khrystyna Serhiyenko, University of Kentucky
  • Melissa Sherman-Bennett, MIT & UC Davis
  • Marcus Spradlin, Brown University
  • Ran Tessler, Weizmann Institute of Science
  • Hugh Thomas, Université du Québec à Montréal
  • Jaroslav Trnka, UC Davis
  • Anastasia Volovich, Brown University


This event will be co-funded by the National Science Foundation.